The invention relates to a method of determining the charge carrier concentration in a doped specimen, notably a semiconductor. The charge carrier concentration for semiconductors is to be understood to mean the electron concentration in the case of n-type semiconductors as well as the hole concentration in the case of p-type semiconductors. Generally speaking, the dope atom concentration in the material follows directly from such a charge carrier concentration.
The invention also relates to an electron beam apparatus for carrying out such a method.
The distribution of dope atoms is of major importance for correct operation of semiconductor elements. The concentration thereof determines the electrical properties of the doped material and the exact distribution thereof co-determines the correct operation of the semiconductor elements. The manufacture of such semiconductor elements involves various process steps which may influence the distribution of the dope atoms, for example thermal treatments. Therefore, it is desirable to have a method of measuring the distribution of the dope atoms so as to check the effect of the process steps; this is desirable not only during the development of the semiconductor elements, but also during critical process steps in their manufacture.
The following problem will be further illustrated on the basis of dope atom distributions in Si (silicon) doped with B (borium), so in a p-type semiconductor material. The present generation of Si semiconductors is so small that a technique such as xe2x80x9csecondary ion mass spectroscopyxe2x80x9d, being renowned for its favorable detection limit, cannot offer the desired lateral resolution. An alternative technique, wherein a Scanning Electron Microscope (SEM) is used to analyze the energy of secondary electrons obtained by bombardment of a specimen (substrate or wafer) by means of electrons and to measure the charge carrier concentration on the basis of the plasmon frequency, is known from JP-A-63/271949. Because the plasmon energy is of the same order of magnitude as that of the secondary electrons, according to the cited publication measurement is performed on the derivative of the energy spectrum, this leads to inadequate accuracy.
It is an object of the invention to provide a method of accurately determining the charge carrier concentration, notably in the case of semiconductors of very small dimensions. This object is achieved according to the invention in that the method of the kind set forth is characterized in that the electron beam emanating from an electron source is made to interact with the specimen, after which an energy spectrum of the electrons is derived from this beam by means of a spectrometer, said spectrum being analyzed so as to derive therefrom the plasmon frequency in the specimen and the charge carrier concentration of the doped material being derived therefrom. In other words, measurement is performed on the primary electrons. The detection efficiency of primary electrons is many times higher than that of secondary electrons, because they fill a much smaller solid angle. Furthermore, analysis of the spectrum of secondary electrons is significantly more difficult, because the plasmon peaks occurring appear against a strong signal background; the energy of at least the first plasmon peak is of the same order of magnitude as the energy of the secondary electrons. Furthermore, it is difficult to separate secondary electrons of an energy near that of the primary electrons from the primary electrons; this necessitates the use of complex and hence expensive equipment.
The energy spectrum is preferably determined by means of an xe2x80x9cElectron Energy Loss Spectroscopyxe2x80x9d (EELS) technique. In as far as the electrons do not lose energy in the specimen, they produce a so-called xe2x80x9czero loss peakxe2x80x9d in the energy spectrum, whereas the electrons which interact with the specimen and hence lose energy generally exhibit one or more plasmon peaks in the energy spectrum.
For a plasmon peak the maximum energy loss Emax derived from the measured energy spectrum can be expressed by the relation:
Emax=[(Ep)2xe2x88x92(xcex94Ep/2)2]xc2xd
wherein Ep represents the plasmon energy and xcex94Ep represents the width of the plasmon peak. Therefrom, the plasmon energy Ep can be determined and, because Ep equals h/2xcfx80.xcfx89p, also the plasmon frequency xcfx89p. The following relation holds approximately for the plasmon frequency xcfx89p:   n  =                    m        ⁢                  xe2x80x83                ⁢                  ϵ          o                            e        2              ⁢          ω      p      2      
wherein m is the mass of an electron, e is the charge thereof, ∈o is the dielectric constant and n is the charge carrier concentration.
Because in the example involving borium-doped silicon the electron concentration n in the specimen consists mainly of the difference between the silicon valence electron concentration nv and the borium hole concentration ng, the value n obtained should be corrected by way of the value of nv. Moreover, for example, because in the case of phosphor-doped silicon the electron concentration n in the specimen consists mainly of the sum of the silicon valence electron concentration nv and the phosphor conductance electron concentration ng, the value n obtained should be corrected by way of the value of nv. These corrections can be determined by calculation or, as is much more accurate, by calibration. Calibration is then performed by applying the method according to the invention to a non-doped specimen or a non-doped part of a doped specimen.
It has been found in practice that the measured plasmon frequency is also dependent on the thickness of the specimen. Therefore, according to the invention the plasmon frequency xcfx89p is corrected for the thickness of the specimen. When the (P)EELS spectrum is measured from the xe2x80x9czero lossxe2x80x9d peak to the plasmon peak, a measure of the thickness can be calculated from the ratio of the two peak heights. Using this thickness, the plasmon frequency can be transformed to a thickness-independent value. It has been found in practice that a mainly linear relationship exists between the plasmon frequency and the thickness of the specimen for B-doped Si: xcfx89p=a.thickness+b(ng). Therein, xe2x80x9caxe2x80x9d is independent of the B concentration ng within the measuring accuracy, but xe2x80x9cbxe2x80x9d is dependent thereon. The previously determined thickness of the specimen can then be used to determine the value of xe2x80x9cbxe2x80x9d from the measured plasmon frequency, and hence also the plasmon frequency for a thickness xe2x80x9czeroxe2x80x9d or the plasmon frequency for a standard thickness of the specimen.
In order to derive an energy spectrum of the primary electrons, interacting with the atoms in the specimen or not, notably an xe2x80x9cElectron Energy Loss Spectroscopyxe2x80x9d (EELS) technique is used. Use is preferably made of xe2x80x9cParallel Electron Energy Loss Spectroscopyxe2x80x9d (PEELS) wherein the output signals of the spectrometer used are simultaneously read out and hence the zero loss peak and the plasmon peak or peaks are measured simultaneously. It is a drawback of the serial reading out of the output channels of the spectrometer that, when variations in time (for example, of the current or voltage) occur in, for example, the spectrometer, the measured positions of essentially the same plasmon peak may differ.
Even though it is possible to determine the energy spectrum of the primary electron beam after it has entered into interaction with the specimen during reflection (where the beam is incident on the sample at an acute angle), the electron beam preferably is made to interact with the specimen in transmission. According to the invention the plasmon frequency, therefore, is determined in a xe2x80x9cTransmission Electron Microscopexe2x80x9d (TEM). When the electron beam is focused on the specimen in a TEM, the charge carrier concentration is determined at that area. The spot size is dependent on the degree of (de)focusing. In the case of a comparatively large spot, the mean charge carrier concentration is determined. However, notably for semiconductors it is very important that the local charge carrier concentration can be determined each time across a given spot size. Therefore, the plasmon frequency is preferably determined in a xe2x80x9cScanning Transmission Electron Microscopexe2x80x9d (STEM).
When in the case of comparatively thick samples a plurality of plasmon peaks occur which, moreover, considerably overlap, it is particularly difficult to determine the peak magnitude, peak width and peak position. In addition to the fact that the method disclosed in the cited Japanese patent application is not sufficiently accurate for determining the doping concentration in extremely small semiconductors, it has not been realized (probably for this reason) that the doping concentration might be derived from the plasmon frequency. However, it has been found that, notably in the case of borium-doped silicon, an adequately accurate doping concentration can be determined when the measured energy spectrum is analyzed entirely by way of a xe2x80x9cfittingxe2x80x9d technique wherein the peak position, the peak height and preferably also the peak width of the xe2x80x9czero loss peakxe2x80x9d and the plasmon peak or peaks are determined. A fitting technique of this kind is known, for example, from xe2x80x9cPress c.s.: Numerical Recipes in Fortran 77, pp. 650 and furtherxe2x80x9d. In the case of comparatively thick specimens it will usually be possible to determine a plurality of plasmons and hence observe a plurality of plasmon peaks in the energy spectrum. Even though these peaks strongly overlap, the successive peak intervals provide enough additional information to enable sufficiently accurate analysis of the spectrum. In the case of comparatively thin specimens, the intensity of the plasmon peak is usually so low that the determination of the peak position and hence the plasmon frequency is insufficiently accurate. Therefore, a somewhat thicker specimen is to be preferred; moreover, a thicker specimen is easier to manufacture.